On λ-invariants of number fields and étale cohomology

Publisher: Cambridge University Press

E-ISSN: 1865-5394|12|1|167-181

ISSN: 1865-2433

Source: Journal of K-Theory, Vol.12, Iss.1, 2013-08, pp. : 167-181

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Abstract

For an odd prime p we prove a Riemann-Hurwitz type formula for odd eigenspaces of the standard Iwasawa modules over F(μp ∞), the field obtained from a totally real number field F by adjoining all p-power roots of unity. We use a new approach based on the relationship between eigenspaces and étale cohomology groups over the cyclotomic ℤ p -extension F of F. The systematic use of étale cohomology greatly simplifies the proof and allows to generalize the classical result about the minus-eigenspace to all odd eigenspaces.